Influenza Bern
Methoods
Incidence and Reproduction number ( R effective)
- Incidence per 1’000 inhabitants
- Rolling average over 3 weeks
Maps - Municipalities
- calculated only for pandemic times:
- 21.06.1918 - 20.09.1918
- 27.09.1918 - 20.06.1919
- 02.01.1920 - 18.06.1920
- 23.12.1921 - 05.05.1922
- 11.01.1924 - 30.05.1924
- 12.12.1924 - 08.05.1925
- Incidence:
- breaks: Jenks Natural Breaks - finds the “best” way to split up the ranges.
- natural breaks minimizes the variation within each color, so the areas within each color are as close as possible in value to each other
- quantile breaks do not work, because there are many zeros in the municipalities from 1920 onwards
- Hotspots:
- local spatial statistic G
- R package: spdep
- returned is a Z-value
- high positive values indicate the posibility of a local cluster of high values
- low relative values a similar cluster of low values
Co-factors for Pandemic 1918/1919
- sum of all cases per municipality for 1918 and 1919
- Incidence per 1’000 inhabitants
- Negative binomial regression to avoid over dispersion
- bivariate maps
The following co-factors were considered:
* Population density
* Altitude * Precipitation -> However,altitude and precipitation are
highly correlated. There is a significant interaction between altitude
and precipitation. For that reason I would take only the altitude as
co-factor for the total number of cases 1918/1919 * TB death *
Proportion of people working in agriculture and industry, I would take
only one (same result only opposite) * Proportion of “Betriebe”, “Anzahl
Arbeiter in den Betriebe”, “PS”. 194 municipalities does not have any
Betriebe * Urbanity, only 3 cities -> not possible to use with this
classification
For bivarite map clustering “quantile”
clustering was used for population density, altitude, precipitation, tb
death and proportion of people working in industry and agriculture.
Since “Betriebe”, “Anzahl Arbeiter in den Betriebe” and
“PS” have a lot of zeros (no Beriebe) “quantile” clustering is not
possible, therefor “jenks” was used.
Canton Bern
Regions of Bern
Incidence
Municipality
1918 First wave
1918-1919 second wave
1920
1922
1924
End 1924 -1925
Co-factors
Population density
Municipality with a higher population density have a significant higher incidence.
##
## Call:
## glm.nb(formula = Sum_date ~ PopDens + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.608201514)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5711 -0.9305 -0.1815 0.4678 2.9240
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.9043444 0.0438796 -43.399 < 2e-16 ***
## PopDens 0.0005417 0.0001802 3.006 0.00265 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.6082) family taken to be 1)
##
## Null deviance: 521.57 on 463 degrees of freedom
## Residual deviance: 515.22 on 462 degrees of freedom
## (11 Beobachtungen als fehlend gelöscht)
## AIC: 5279.4
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.608
## Std. Err.: 0.102
##
## 2 x log-likelihood: -5273.438
## PopDens breaks (x-axis):
## style: quantile
## [0,69.362) [69.362,122.6337) [122.6337,3306.645]
## 155 154 155
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,90.57187) [90.57187,193.4673) [193.4673,815.047]
## 158 158 159
Altitude
There is a significant correlation between the altitude and the incidence. The higher the municipality, the lower the incidence.
##
## Call:
## glm.nb(formula = Sum_date ~ HöheüM + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.605654021)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5418 -0.9377 -0.1644 0.4215 3.5664
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.4731187 0.1314764 -11.204 < 2e-16 ***
## HöheüM -0.0005792 0.0002035 -2.846 0.00443 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.6057) family taken to be 1)
##
## Null deviance: 534.35 on 473 degrees of freedom
## Residual deviance: 525.81 on 472 degrees of freedom
## (1 Beobachtung als fehlend gelöscht)
## AIC: 5373.9
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.606
## Std. Err.: 0.101
##
## 2 x log-likelihood: -5367.883
## HöheüM breaks (x-axis):
## style: quantile
## [328,511) [511,655.3333) [655.3333,1356]
## 157 159 158
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,90.57187) [90.57187,193.4673) [193.4673,815.047]
## 158 158 159
Precipitation
There is a significant correlation between Precipitation and the incidence. The more precipitation, the lower the incidence. Altitude and precipitation show a significant interaction. I would not show precipitation for total cases per municipility.
##
## Call:
## glm.nb(formula = Sum_date ~ Total_rain + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.631214115)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.6272 -0.9140 -0.1511 0.4149 3.5085
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -4.913e-01 3.739e-01 -1.314 0.188896
## Total_rain -2.352e-05 6.500e-06 -3.619 0.000295 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.6312) family taken to be 1)
##
## Null deviance: 528.59 on 463 degrees of freedom
## Residual deviance: 514.84 on 462 degrees of freedom
## (11 Beobachtungen als fehlend gelöscht)
## AIC: 5272.2
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.631
## Std. Err.: 0.104
##
## 2 x log-likelihood: -5266.180
## Total_rain breaks (x-axis):
## style: quantile
## [44667.56,53635.27) [53635.27,59236.5) [59236.5,83922.42]
## 155 154 155
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,90.57187) [90.57187,193.4673) [193.4673,815.047]
## 158 158 159
Tuberculosis death
No evidence of a significant association, but trend that high TB deaths lead to lower incidence.
##
## Call:
## glm.nb(formula = Sum_date ~ TB + offset(log(Population)), data = data_inc,
## link = "log", init.theta = 1.66651015)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.0214 -0.9303 -0.1777 0.4702 2.8453
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.735347 0.092073 -18.847 <2e-16 ***
## TB -0.004045 0.003396 -1.191 0.234
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.6665) family taken to be 1)
##
## Null deviance: 510.06 on 461 degrees of freedom
## Residual deviance: 508.53 on 460 degrees of freedom
## (13 Beobachtungen als fehlend gelöscht)
## AIC: 5239.3
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.667
## Std. Err.: 0.106
##
## 2 x log-likelihood: -5233.349
## TB breaks (x-axis):
## style: quantile
## [0,19.3) [19.3,28.83333) [28.83333,75.9]
## 151 157 154
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,905.7187) [905.7187,1934.673) [1934.673,8150.47]
## 158 158 159
people working in agriculture
There is no evidence for a significant association between the proportion of people working in agriculture and incidence.
##
## Call:
## glm.nb(formula = Sum_date ~ Lws_prop + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.584206326)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5657 -0.9249 -0.1971 0.4560 2.8253
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.784345 0.085843 -20.786 <2e-16 ***
## Lws_prop -0.001947 0.003668 -0.531 0.596
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.5842) family taken to be 1)
##
## Null deviance: 524.52 on 471 degrees of freedom
## Residual deviance: 524.22 on 470 degrees of freedom
## (3 Beobachtungen als fehlend gelöscht)
## AIC: 5354.3
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.5842
## Std. Err.: 0.0994
##
## 2 x log-likelihood: -5348.2770
## Lws_prop breaks (x-axis):
## style: quantile
## [0.456621,16.74419) [16.74419,25.64935) [25.64935,72.72727]
## 157 157 158
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,90.57187) [90.57187,193.4673) [193.4673,815.047]
## 158 158 159
people working in industry
There is no evidence for a significant association between the proportion of people working in agriculture and incidence.
##
## Call:
## glm.nb(formula = Sum_date ~ Gew_prop + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.583275675)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5747 -0.9251 -0.1909 0.4519 2.7685
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.8378980 0.0766667 -23.973 <2e-16 ***
## Gew_prop 0.0008383 0.0044558 0.188 0.851
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.5833) family taken to be 1)
##
## Null deviance: 524.23 on 471 degrees of freedom
## Residual deviance: 524.19 on 470 degrees of freedom
## (3 Beobachtungen als fehlend gelöscht)
## AIC: 5354.5
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.5833
## Std. Err.: 0.0993
##
## 2 x log-likelihood: -5348.5350
## Gew_prop breaks (x-axis):
## style: quantile
## [0,10.57402) [10.57402,18.25813) [18.25813,55.44958]
## 157 157 158
## Sum_Inc breaks (y-axis):
## style: quantile
## [0,90.57187) [90.57187,193.4673) [193.4673,815.047]
## 158 158 159
Industrial companies
There is no evidence for a significant association between the numbers of industrual companies per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “companies” in two (or more groups (e.g. none, same, a lot)) give the same result.
##
## Call:
## glm.nb(formula = Sum_date ~ Betriebe_prop + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.565436317)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5574 -0.9140 -0.1872 0.4503 2.7331
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.83921 0.04183 -43.970 <2e-16 ***
## Betriebe_prop 0.01106 0.02139 0.517 0.605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.5654) family taken to be 1)
##
## Null deviance: 529.67 on 474 degrees of freedom
## Residual deviance: 529.42 on 473 degrees of freedom
## AIC: 5390.1
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.5654
## Std. Err.: 0.0981
##
## 2 x log-likelihood: -5384.0630
## Betriebe_prop breaks (x-axis):
## style: jenks
## one of 11,325 possible partitions of this variable into 3 classes
## [0,1.267427] (1.267427,4.166667] (4.166667,9.393451]
## 363 80 32
## Sum_Inc breaks (y-axis):
## style: jenks
## [0,150.7353] (150.7353,346.7742] (346.7742,815.047]
## 260 185 30
Total workers
There is no evidence for a significant association between the numbers of workers per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “total workers” in two (or more groups (e.g. none, same, a lot)) give the same result.
##
## Call:
## glm.nb(formula = Sum_date ~ Arbeiter_prop + offset(log(Population)),
## data = data_inc, link = "log", init.theta = 1.566256701)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5565 -0.9201 -0.1972 0.4557 2.7423
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.842947 0.041203 -44.728 <2e-16 ***
## Arbeiter_prop 0.003399 0.004508 0.754 0.451
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.5663) family taken to be 1)
##
## Null deviance: 529.93 on 474 degrees of freedom
## Residual deviance: 529.41 on 473 degrees of freedom
## AIC: 5389.8
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.5663
## Std. Err.: 0.0981
##
## 2 x log-likelihood: -5383.7950
## Arbeiter_prop breaks (x-axis):
## style: jenks
## [0,6.944444] (6.944444,21.84497] (21.84497,59.08184]
## 391 58 26
## Sum_Inc breaks (y-axis):
## style: jenks
## [0,150.7353] (150.7353,346.7742] (346.7742,815.047]
## 260 185 30
PS
There is no evidence for a significant association between PS per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “PS” in two (or more groups (e.g. none, same, a lot)) give the same result.
##
## Call:
## glm.nb(formula = Sum_date ~ PS + offset(log(Population)), data = data_inc,
## link = "log", init.theta = 1.571974792)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5617 -0.9130 -0.1840 0.4496 2.7773
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.842e+00 3.773e-02 -48.83 <2e-16 ***
## PS 7.967e-05 5.044e-05 1.58 0.114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(1.572) family taken to be 1)
##
## Null deviance: 531.74 on 474 degrees of freedom
## Residual deviance: 529.37 on 473 degrees of freedom
## AIC: 5387.9
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 1.5720
## Std. Err.: 0.0985
##
## 2 x log-likelihood: -5381.9420
## PS_prop breaks (x-axis):
## style: jenks
## one of 11,026 possible partitions of this variable into 3 classes
## [0,27.50432] (27.50432,124.0506] (124.0506,380.5073]
## 452 22 1
## Sum_Inc breaks (y-axis):
## style: jenks
## [0,150.7353] (150.7353,346.7742] (346.7742,815.047]
## 260 185 30